Question: Factor completely. $49c^2+70cd+25d^2=$
Solution: $\begin{aligned} &\phantom{=}49 c ^2 + 70 c d + 25 d ^2 \\\\ &= ({7 c })^2 + 2({7 c })({5 d })+({5 d })^2 \end{aligned}$ Using the square of a sum pattern: $\begin{aligned} &\phantom{=}({7 c })^2 + 2({7 c })({5 d })+({5 d })^2 \\\\ &=({7 c } + {5 d })^2 \end{aligned}$ In conclusion, $49 c ^2 + 70 c d + 25 d ^2=(7 c + 5 d )^2$ Remember that you can always check your factorization by expanding it.